Journal of Statistical Physics, Vol. 23, No. 6, 1980. p. 773-782.
Exact results are obtained for the annealed, dilute, q-component Potts model on the decorated square lattice. The phase diagram is found to consist of a high-temperature region, a low-temperature region, and a two-phase region in between which arises only for q > 4; exact expressions for the phase boundary and the critical probability are derived. At the critical point the specific heat is generally finite and has a cusp; the slope of the cusp is finite for q = 4 and infinite (vertical) for q = 2 and 3.